Final answer:
William Randolph Hearst and Joseph Pulitzer were the newspaper owners who sensationalized the troubles in Cuba through yellow journalism in their respective papers, the New York Journal and the New York World, to increase circulation and sway public opinion.
Step-by-step explanation:
The two famous newspaper owners who wrote about the troubles down in Cuba were William Randolph Hearst of the New York Journal and Joseph Pulitzer of the New York World. These publishers engaged in a form of journalism known as yellow journalism, using sensational headlines and stories with little factual support to increase their newspapers' circulation and influence public opinion. Their reporting on Cuba's fight for independence and the Spanish-American War are prime examples of this media strategy. Pulitzer and Hearst competed for readership using tactics such as eye-catching headlines, pictures, and inducing emotional responses, which often eschewed rigorous journalistic standards.